Question

Can someone please help me this is literally making no sense. I've tried to learn this but I suck at math.
Solve the inequality and graph the solution.
8|x+3/4|<2

Answer 1

first off, keep in mind that |something| really means
+(something) AND -(something)

so you really end up with 2 answers, or 2 values for "x"
\({\bf 8\left|x+\cfrac{3}{4}\right|< 2\\
\textit{dividing each side by 8}\\
\left|x+\cfrac{3}{4}\right|<\cfrac{2}{8} \implies \left|x+\cfrac{3}{4}\right|<\cfrac{1}{4}\\
-----------------\\
\left|x+\cfrac{3}{4}\right|<\cfrac{1}{4} \implies }
\begin{cases}
+\left(x+\cfrac{3}{4}\right)<\cfrac{1}{4} \implies &x+\cfrac{3}{4}<\cfrac{1}{4}\\
-\left(x+\cfrac{3}{4}\right)<\cfrac{1}{4} \implies &-x-\cfrac{3}{4}<\cfrac{1}{4}
\end{cases}
\)

Answer 2

omg thank you so much! T_T

Answer 3

yw